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极值预测在自然灾害防御、化工安全生产、金融风险管控等许多安全场景中具有重要应用,然而,由于混合类型事件的影响,传统极值预测方法往往无法有效处理数据中不同分布所引起的问题.为此,本文提出了一种基于混合Copula函数结合聚类算法的极值风速预测方法.在此方法中,首先采用聚类算法自适应地将风速块最大数据集划分为不同簇,并获取每个簇的最佳边缘分布;然后,利用混合Copula函数连接各簇的边缘分布,采用粒子群优化算法最小化KL散度,从而确定混合Copula函数的权重,最终实现在特定重现期下的风速极值预测.为避免过拟合和欠拟合,采用两折交叉验证对模型进行验证与调优.实证结果表明,本文提出的模型在混合分布下能够显著提高极值预测的准确性和可靠性,在风速等气象数据的极值预测中,相较于传统方法具有更高的预测精度和稳定性.本文方法不仅为风速数据等领域的极值分析提供了有力工具,也为其他混合分布数据的极值预测提供了新的思路和方法.
Abstract：Extreme value prediction plays a vital role in various safety-critical scenarios, including natural disaster defense, chemical production safety, and financial risk management. However, due to the presence of mixed-type events, traditional extreme value prediction methods often struggle to effectively capture the mixed distribution characteristics inherent in the data. To address this, this paper proposes an extreme wind speed prediction method based on a mixed copula function combined with a clustering algorithm. In this method, a clustering algorithm is first employed to adaptively group the block maxima dataset of wind speed into distinct clusters, and the optimal marginal distribution for each cluster is subsequently obtained. A mixed copula function is then constructed to link the marginal distributions of each cluster, and the particle swarm optimization algorithm is utilized to minimize the KL divergence, thereby determining the weights of the mixed copula function, which ultimately enables the prediction of wind speed extremes for specific return periods. To avoid overfitting and underfitting, 2-fold cross-validation is used for model validation and tuning. The empirical results demonstrate that the proposed model significantly improves the accuracy and reliability of extreme value prediction under mixed distributions, exhibiting higher predictive accuracy and greater stability in forecasting meteorological extremes, such as wind speed, compared to traditional methods. This study not only provides a powerful tool for extreme value analysis in fields involving wind speed data but also offers new insights and methodologies for predicting extremes in other datasets characterized by mixed distributions.
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基本信息:
DOI：10.19943/j.2095-3070.jmmia.2026.01.04
中图分类号:P412.16;P457.5
引用信息:
[1]董胜男,刘云冰,何晓霞,等.基于混合Copula函数和聚类算法的极值风速预测[J].数学建模及其应用,2026,15(01):31-41.DOI:10.19943/j.2095-3070.jmmia.2026.01.04.
基金信息:
湖北省重点实验室开放项目(Y202201)
2026-03-15
2026-03-15